The conformal window in QCD and supersymmetric QCD

TL;DR

This paper investigates the conformal windows of QCD and SQCD, showing that QCD's infrared fixed point is perturbative throughout its conformal window, unlike SQCD, and explores duality and perturbative interpolation between theories.

Contribution

It demonstrates that QCD's infrared fixed point remains perturbative across its conformal window and introduces a method to interpolate between electric and magnetic theories in SQCD.

Findings

QCD's IR fixed point is perturbative in the entire conformal window.

No duality analog exists in QCD due to perturbative IR fixed point.

Interpolation between electric and magnetic theories is possible for certain perturbative quantities.

Abstract

In both QCD and supersymmetric QCD (SQCD) with N_f flavors there are conformal windows where the theory is asymptotically free in the ultraviolet while the infrared physics is governed by a non-trivial fixed-point. In SQCD, the lower N_f boundary of the conformal window, below which the theory is confining is well understood thanks to duality. In QCD there is just a sufficient condition for confinement based on superconvergence. Studying the Banks-Zaks expansion and analyzing the conditions for the perturbative coupling to have a causal analyticity structure, it is shown that the infrared fixed-point in QCD is perturbative in the entire conformal window. This finding suggests that there can be no analog of duality in QCD. On the other hand in SQCD the infrared region is found to be strongly coupled in the lower part of the conformal window, in agreement with duality. Nevertheless, we show that it is possible to interpolate between the Banks-Zaks expansions in the electric and magnetic theories, for quantities that can be calculated perturbatively in both. This interpolation is explicitly demonstrated for the critical exponent that controls the rate at which a generic physical quantity approaches the fixed-point.